How to Simplify Roots

When you work with roots in an equation, you often need to simplify them. There are two methods: the quick, sort of intuitive method, and a slightly longer method. The quick method of simplification works only with some roots, like

The quick method works for the square root of 300 because it’s easy to see a large perfect square, 100, that goes into 300. Because 300 equals 100 times 3, the 100 comes out as its square root, 10, leaving the 3 inside the square root. The answer is thus

It’s not as easy to find a large perfect square that goes into 504, so you’ve got to use the longer method to solve it.

Break 504 down into a product of all of its prime factors.

Circle or identify each pair of numbers.

For each pair you identify, take one number out.

Simplify.

The last thing about roots is that by convention, you don’t leave a root in the denominator of a fraction — it’s a silly, anachronistic convention, but it’s still being taught, so here it is.